Discrete event distribution sampling apparatus and methods

ABSTRACT

Locations of the origins of “discrete events,” e.g., photons or other units of radiant energy are acquired from a specimen with reference to a scan frame or other region of interest of the specimen. The location of origin of a discrete event can be determined from the corresponding location datum as derived from a scan-drive signal, a positional feed-back signal, or by a point in time during a unit of sampling time (“image-acquisition period”) at which the event is detected. A probability-density function (PDF) is associated with the detected locations. Summing or other processing of the PDFs is performed to produce imageable data. From the data, images can be produced that require fewer discrete events to converge to an ideal density distribution associated with an image feature than required by pixel-based binning methods. Stored data can be mapped into pixels or voxels of a display or otherwise processed, including post hoc processing.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of and claims priority to andthe benefit of U.S. patent application Ser. No. 11/597,028, filed onNov. 17, 2006, which claims priority to and the benefit of U.S.Provisional Application No. 60/573,459, filed on May 20, 2004, both ofwhich are incorporated herein by reference in their respectiveentireties.

FIELD

This invention concerns, inter alia, high-sensitivity imaging systems,especially optical systems for sensing radiation, including but notlimited to reflected radiation, radiation produced by fluorescence,radiation produced by chemiluminescence, and transmitted radiation. Theradiation can be in the form of photons or particles (e.g., electrons).Photons are not limited to visible-light photons.

BACKGROUND

Detecting photons and producing images from a scanned field of view havebeen performed to produce electronic outputs representing the field ofview of an instrument, such as a laser-scanning confocal microscope(LSCM). In this regard, the term “photon” means a unit ofelectromagnetic energy irrespective of its position in the spectrum,e.g., visible or invisible radiation. In quantum physics, a photon ischaracterized as an entity having particle and wave characteristics.Other forms of radiation, such as electrons, may also exhibit bothparticle and wave characteristics. The nature of the present inventionand the manner of its use are not dependent on whether the radiantevents are photons or other types of elementary particles.

In one prior-art optical-detection technique, photons are directed by aconfocal imager in a confocal microscope to be sensed by a detector. Aconfocal imager comprises a point-source of light that illuminates aspot on or in a specimen. In order to illuminate an entire specimen withthe spot, the light source is scanned across the specimen by abeam-steering device using scanners that are well known in the art. Anilluminated spot is imaged onto a detector through a pinhole. Detectorscomprise, for example, avalanche photodiode arrays or photomultipliertubes or arrays of such devices.

The light source, the illuminated spot, and the detector have the samefoci and are placed in conjugate focal-planes. Hence, they are“confocal” to each other.

The diameter of the pinhole is preferably matched to the illuminatedspot through the optics situated between them. Because a small spot isilluminated and detected through a small aperture, light imaged onto thedetector comes predominantly from the plane in focus within or on thespecimen. The detector produces output pulses indicative of the detectedphotons.

The output pulses from the detector are processed to provide informationsuch as time-correlated photon-counting histograms and image-generationin conventional laser scanning. In conventional imaging systems,however, photons obtained over each of a number of successive, selectedequal time periods defined by a pixel clock are used to generate arespective intensity value assigned to each pixel (a pixel is atwo-dimensional area of a portion of an image). Photon counts are“binned,” that is, accumulated as groups, during each sampling period;each group corresponds to a pixel location of an image display. (It isnoted that the term “binning” is sometimes used to denote lumping pixelstogether, e.g., as during use of a CCD camera. This is a different useof “binning” than the use of the term herein.) In this manner, acomputer builds up an entire image one pixel at a time to produce atwo-dimensional image often made up of multiple thousands or millions ofpixels. For three-dimensional imaging, successive two-dimensional layersof a specimen are scanned, and the computer builds up an imagecomprising voxels (three-dimensional pixels).

In producing a conventional image, a scan rate is selected. As scan rateincreases, fewer photons per pixel per scan are accumulated, and theintensity of the pixels and their signal-to-noise ratios thereforedecrease. As a result, prior-art pixel-based imaging systems faceconstraints in scan rate with regard to the quality of output signal tobe produced. Physical and mechanical constraints, such as the rate atwhich a scanner can move, are also present. In addition, the number ofphoton counts in a specimen affects other parameters of image qualityrelating to intensity. These parameters include signal-to-noise ratio.

As a result, pixel-based scanning typically allows for reducedflexibility in experiment design. Resolution of the location of eachphoton is limited to the dimensions of a pixel or voxel as applicable.The amount of excitation illumination required for the output data toreach convergence of features of sensed images is proportional to thenumber of photons that must be produced to provide data sufficient toreach this convergence. When pixels are of smaller dimension andtherefore provide fewer photons per scan, specimens would have to besubjected to excitation radiation a larger number of times or the samenumber of times (but for longer time intervals) than if the pixels werelarger.

The requirement for greater illumination has functional drawbacks. Inexample applications involving fluorescent specimens, many fluorescentmolecules under test can fluoresce only a limited number of times. Atsome point, response to excitation radiation ceases, and an effect knownas photo-bleaching occurs. Over-illumination also presents anotherdrawback. With measurements made in vivo, emission of photons fromtissue produces free radicals, which can damage cells. Therefore,over-illumination of tissue can result in photo-toxicity.

A limitation of typical prior-art techniques is that they are opticallybased. Optically based techniques have an inherent limit of resolutionknown as a diffraction limit, which may be ˜0.6λ, where λ is thewavelength of the illuminating light. The resolving power of a lens isultimately limited by diffraction effects. The lens's aperture is a“hole” that is analogous to a two-dimensional version of the single-slitexperiment. Light passing through the lens interferes with itself,creating a ring-shaped diffraction pattern known as the Airy pattern,that blurs the image. An empirical diffraction limit is given by theRayleigh criterion:

${{\sin \; \theta} = {1.22\frac{\lambda}{D}}},$

where θ is the angular resolution, λ is the wavelength of light, and Dis the diameter of the lens. A wave does not have to pass through anaperture to diffract. For example, a beam of light of a finite sizepassing through a lens also undergoes diffraction and spreads indiameter. This effect limits the minimum size d of spot of light formedat the focal point of a lens, known as the diffraction limit:

${d = {2.44\lambda \frac{f}{a}}},$

where λ is the wavelength of the light, f is the focal length of thelens, and a is the diameter of the beam of light, or (if the beam isfilling the lens) the diameter of the lens. Techniques that utilizeso-called far-field or propagating-wave optics do not afford theopportunity to obtain resolution beyond the diffraction limit.

SUMMARY

The Applicants have discovered, inter alia, methods for retaining data,concerning the locations of discrete events associated with a specimen.Such data are conventionally lost in prior-art pixel-based imagingtechniques. For example, conventional methods involving “binning” ofphotons typically result in loss of data. Also, in conventional pixel-or voxel-based sampling systems, more photons are usually detected thanotherwise would be necessary if the system did not lose data from use ofthe pixel-sampling paradigm. In a conventional pixel-based samplingparadigm, photons collected during a predefined pixel clock interval aresummed. This summing results in the loss of spatial and temporalinformation for individual photons. Other information could take manyforms, such as, for example, spectral or energy level.

Various system and method embodiments disclosed herein are called“Discrete Event Detection Sampling,” or “DEDS,” systems and methods.DEDS encompasses “REDS” or “Radiant Event Detection Sampling” and “PEDS”or “Photon Event Detection Sampling,” the latter being an appropriatedesignation whenever the radiant events involve photons. DEDSencompasses methods for producing imageable data on discrete eventsassociated with a specimen. Events that are “associated with” a specimeninclude events that originate from the specimen or result from aninteraction with the specimen. The discrete events can be, by way ofexample and not intended to be limiting, respective photons or groups ofphotons, respective units of radiation, and/or respective particles orgroups of particles. Individual discrete events are detected during animage-acquisition period and are assigned a respective positionindicating their site of origin in or on the specimen being imaged. Thepositions (e.g., x- and y-positions) can be obtained from positionsignals indicating the specific site in or on the specimen at theinstant the event is detected, or can be obtained from time-basedsignals indicating the location of the imaged sites. The positionsobtained for events occurring during the acquisition period can bestored in, e.g., a file in a computer. During formation of the image,each relevant position is assigned a distribution determined by aprobability-density function (PDF), which expresses the uncertaintyassociated with its determination. The respective distributions for thedetected. events are summed to form the image. The most appropriate PDFmay be calculated or measured empirically and is determined by, forexample, the nature of the instrumentation used to elicit and/or detectthe events, the methods used for obtaining the image, the properties ofthe specimen, and the nature of the discrete events involved.

DEDS can be implemented in both scanning and non-scanning formats. InScanning DEDS (SDEDS) the specimen to be imaged is scanned by moving thespecimen and/or a detector or detecting probe relative to each other.For example, in certain types of REDS methods, an interrogation beam(e.g., of photons or particles) and/or the specimen are moved relativeto each other. During an image-acquisition period a signal designatingthe position of origin, within or on the specimen, of each detectedevent is recorded and assigned a PDF. Individual PDFs are summed to forman image.

Certain DEDS embodiments do not require scanning the specimen withinterrogating energy (e.g., a beam of light or of electrons). TheseNon-Scanning DEDS (NSDEDS) embodiments desirably utilize detectorscomprising multiple discrete detection units that are small in sizerelative to the size of the distribution assigned to the PDF. Thus, therespective positions of the origins of the discrete, detectable eventscan be placed accurately in the image. The individual discrete eventsdetected by each detection unit during an image-acquisition period arecounted and assigned an appropriate PDF. In NSDEDS the position oforigin of a discrete event can be designated as the position of theindividual detection unit.

DEDS also encompasses embodiments in which the discrete events ariseeither spontaneously or without the need for input of interrogatingenergy. In these embodiments the position information required for eachdiscrete event desirably is derived from an element(s) of the detectionpathway, such as moving the specimen relative to the detectors (e.g.,using scan mirrors or moving a stage on which the specimen is placed),moving a detecting probe relative to the specimen, or by using adetector with unitary detection elements of small size. The distributionused for the PDF reflects, inter alia, the nature of the discrete eventsand the properties of the detection pathway. In contrast, wheninterrogation energy is used, the PDF can also reflect the manner inwhich the interrogation energy interacts with the specimen, as well asthe nature of the discrete events caused by the interaction.

In view of these fundamental aspects of DEDS, the subject methods andapparatus are useful for various diverse types of imaging systems andare not limited to confocal systems such as, for example, point-scanningconfocal microscopy systems. The subject methods and apparatus are alsonot limited to methods and systems employing excitation or interrogationenergy. The methods and apparatus also can be used to form images with,for example, transmitted light produced by the specimen but not inresponse to an excitation beam or interrogation beam. Scan mirrors canbe used for directing light from specific regions of a specimen througha pinhole to a detector, wherein relevant position information isobtained for the detected discrete events (e.g., photons). The methodsand apparatus also are not limited to microscope-based detectionsystems.

In accordance with certain embodiments of the present invention,apparatus and methods are provided for use with a scanned specimen thatemits photons or other form of radiation during image-acquisitionperiods in which the location, or site, of the origin of individualphotons, or sets of photons, are determined and recorded. The locationsof the sources of individual photons or sources of photons are acquiredin a “pixel-less” manner to yield positional information for eachdetected photon. The locations of the origins of the photons areacquired with reference to a scan frame that may be defined as a singleinstance of a scan pattern.

In one embodiment the scanner traverses the scan pattern over animage-acquisition period. During each successive scan, the scanner mayhave the same location at the same elapsed time from the beginning ofthe image-acquisition period. Therefore, during a scan, a current x-ylocation of the scanner may have a one-to-one correspondence with avalue of a signal associated with scan position. One such signal may bea value of input to a scan driver. Another such signal may be elapsedtime from the beginning of a scan. By measuring elapsed time in relationto the beginning of an image-acquisition period, the position of thescanner may be determined. Another such signal may be values of positionfeedback from the scan device.

Elapsed time may also be measured from a time the scanner has a knownlocation rather than the beginning of a scan. The time of occurrence ofdetection of each photon or other discrete event is registered. Thelocation on the specimen from which a photon, for example, was emittedis inferred from the location of the scanner at the time at which thephoton is detected.

Whenever data concerning position rather than data concerning time areused, the true position of a scanner desirably is tracked independentlyof whether the scanner is following a scan-command signal in a faithfulmanner. In this case, the scanner can be driven at a frequency thatexceeds the linear range of its amplitude/phase-frequency relationshipsto obtain greater scanning velocities.

Certain embodiments measure each discrete-event position by a positionfunction associated with the position. An exemplary position function isevent-probability density. The event PDFs are summed, which can requirefewer discrete events to converge to an ideal density distributionassociated with an image feature than are required using conventionalpixel-based binning methods. Consequently, a smaller number of discreteevents may be counted to yield increased spatial resolution and adecreased uncertainty concerning the sites of origin of the detecteddiscrete events. Sensitivity of measurement also can be improved. Sincefewer discrete events need be detected for a given resolution, lessexcitation illumination of a specimen to produce the discrete events(e.g., emission of photons) is required than with conventionalpixel-based binning methods. The technique thus can eliminate or reduceover-irradiation of specimens and its concomitant adverse effects.

In certain embodiments, image frames may be constructed by summing thespatial distribution of photons or other discrete events over anyuser-selected time period rather than the specific period of apre-selected pixel or voxel. Images can be displayed in raster spaceafter they are stored digitally. Consequently, any imprecisionintroduced by the display process need not adversely affect theprecision of the collected data. The original precise location dataremain available in the digital storage.

Since some embodiments can provide high resolution in scan location,these embodiments also can provide high resolution in photon, particle,or other discrete-event location. In one embodiment, photon locationcorresponds to an analog signal that is converted to a digital signalhaving a pre-selected number of bits. This number of bits can beselected so that the generated image can be based in effect onphoton-location data having a number of bits corresponding to aresolution of several megapixels per image or more in display space.Quality of a displayed image is limited only by the quality of displayapparatus and not by the quality of the data.

In other embodiments, intervals between detections of individualdiscrete events are recorded. Various points in time displaced by equalintervals may each correspond to a milepost location of a scan. A“milepost location” is a predetermined, known location in the scan thatis reached at a specific time within the image-acquisition period. Thelocation of detected events can be calculated by interpolation betweenthe milepost locations. Discrete events are recorded at a rate that isdependent on the number of events detected. Scan-rate need not belimited by the number of detected events expected to be counted in orderto achieve a particular intensity and signal-to-noise (S/N) ratio as istypical in the case of conventional pixel-based sampling.

Alternatively, a signal may be indicative of the x-y position of thescan. The signal can, for example, comprise a monotonically increasingdc signal, in which the amplitude of the signal corresponds to aposition of a scanned beam. A detector-output indicative of detection ofa discrete event in one form triggers a sample-and-hold circuit to storethe amplitude. The stored amplitude can be recorded. The amplitude canbe converted to a corresponding digital value indicative of the preciselocation of the center of the beam (the location having a maximumlikelihood of generating the detected event). A signal can be generatedthat is indicative of the time of detection of a discrete event and usedto determine event location. Other techniques for determining theposition of the scan may be used, including use of a clock or a counteractivated from the beginning of the scan or other milestone.

For further precision, in certain embodiments the effect of variouspossibly interfering phenomena may be reduced or eliminated. Thesephenomena can include sampling delays that may occur in the acquisitionof x-y position information and discrete-event detection, anddifferences between the positions indicated by the signal indicative ofscanner positions and actual scanner positions. Examples of other suchphenomena include the result of inertia of a scanning element or torquein an arm that rotates to drive a scanning component. Torque can resultin different angular positions of opposite ends of a drive arm. Bytaking these types of phenomena into account, precision may be evenfurther improved in certain embodiments.

In some embodiments, discrete-event counting may take place at high scanrates without the need to account for the number of event counts in aspecimen. Image frames in raster space can be generated after the countsare registered and location data are stored. Using a single data set,dynamic events can be viewed to observe changes occurring over time bycomparing images formed from sequential sample frames. Alternatively,discrete events (especially of a dynamic nature) can be viewedstatically on different time scales.

Availability of complete sets of data in time and space can enablefurther forms of processing of the data, including post-hoc analysis,irrespective of acquisition time. Post-hoc analysis of the data canallow further analysis of the specimen, even after the specimen hasbecome either unavailable or unresponsive to further excitationradiation.

In some embodiments, since multiple discrete events are acquired andstatistical approaches are used to determine spatial locations of eventclusters, measurement is not limited by the diffraction limit, such asdefined by the Rayleigh criterion (0.6λ/NA) inherent in opticalmeasurements. Consequently, certain embodiments can provide finerresolution than available from conventional imaging apparatus in whichthe resolution is limited by the diffraction limit.

It will be apparent from the foregoing that DEDS, REDS, and PEDS providecertain advantages over conventional pixel-based binning methods. Theseinclude: (a) since fewer discrete events are required to achieve thesame S/N ratio as conventionally, the diameter of a pinhole (if used)upstream of the event detector can be decreased to improve opticalsectioning further; (b) greater scan-rates can be used with the sameintensity of excitation radiation, if used; (c) equivalent scan-ratescan be used with a reduced intensity of excitation radiation, if used;(d) with the same intensity of excitation radiation, if used, a greaternumber of scans can be averaged to increase the S/N ratio of the image;(e) the centroid position of a specimen can be determined to asub-diffraction limit more rapidly since fewer detected events (e.g.,photons) are required; (f) more efficient image formation requiringfewer detected events (e.g., photons) results in decreasedphoto-bleaching and photo-toxicity of the specimen; and (g) generallyany time an increased S/N ratio is beneficial.

The foregoing is a brief summary of characteristics of certainembodiments of the present invention. This Summary is not exhaustive;additional features and advantages of various embodiments will becomeapparent as this specification proceeds. In addition, it is to beunderstood that embodiments of the invention need not necessarilyaddress all issues noted in the Background nor include all features oradvantages noted in this Summary or in the balance of thisspecification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an apparatus, according to the firstrepresentative embodiment, in which signals indicative of scan positionsare produced as photon events are detected. The photon events arestimulated by radiating the specimen using a laser beam.

FIG. 2 is a flow diagram of an embodiment of a method that can beperformed using the apparatus shown in FIG. 1.

FIG. 3 consists of FIGS. 3( a) and 3(b), in which FIG. 3( a) illustratesphotons that have been detected and their positions mapped in one degreeof freedom, and FIG. 3( b) illustrates an exemplary sum ofprobability-density functions (PDFs) of the photons in FIG. 3( a).

FIG. 4 consists of FIGS. 4( a) and 4(b), in which FIG. 4( a) illustratesphotons that have been detected as being associated with an imagefeature, and FIG. 4( b) represents an exemplary summation of the PDFs ofthe positions of the photons of FIG. 4( a).

FIG. 5 is an illustration of data collected in an embodiment in whichtime intervals between pulses are measured in order to determinelocations of corresponding photons.

FIG. 6, consisting of FIGS. 6( a), 6(b) and 6(c), illustrates mapping ofsensed positions into display raster space.

FIG. 7 is a block diagram of an apparatus embodiment, according to thefourth representative embodiment, that detects radiant events occurringin or on a specimen without having to expose the specimen to aninterrogating or energizing beam.

FIG. 8 is a scatter plot, discussed in Example 4, of signal-to-noiseratio (“SNR,” which is the signal from the specimen (signal_(spec))divided by the standard deviation of the signal obtained from abackground region (noise_(bkg))) values (denoted on the ordinate), asmeasured for images formed from the same image-data sets containing theregistered locations of detected photons using either PEDS (darkdiamonds) or conventional binning (lighter squares). Uniformlyfluorescent, 1.9-μm diameter polystyrene beads were imaged usingincreasing excitation-light intensities to produce a range of photoncounts (abscissa) in a region of interest (ROI) placed within theboundaries of the bead and used to collect the specimen signal values.Background noise values were obtained as the standard deviation of themean photon-flux signal in a ROI of identical size placed sufficientlydistant from the bead so that the recorded values were not influenced byphotons coming from photons emitted by fluorophores in the bead.

FIG. 9 is a scatter plot, obtained in Example 4, of SNR(signal_(spec)/noise_(spec)) values (ordinate) measured for imagesformed from the same photon-event files using either PEDS (darkdiamonds) or conventional binning (lighter squares). A uniformreflective surface consisting of tungsten deposited on silicon wasimaged using increasing excitation-light intensities to produce a rangeof photon counts (abscissa) in a region of interest (ROI) placed in thecenter of the image and used to define the area from which both thespecimen signal and specimen signal noise (standard deviation of meanspecimen signal values) values were measured. Individual values areindicated by the symbols, while the lines represent a power function fitto these values.

FIG. 10 depicts results, discussed in Example 5, of experiments in whichactin filaments in chemically preserved cells were imaged.Photon-position data sets were obtained from the same specimen regionusing three different illumination-light intensities, and images fromeach data set were formed using PEDS (bottom row) or conventionalbinning (top row). SNR (signal_(spec)/noise_(bkg)) values andexcitation-light intensities (I) are provided.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following disclosure is set forth in the context of representativeembodiments that are not intended to be limiting in any way.

Discrete Event Detection and Sampling

Various system and method embodiments within the scope of thisdisclosure are generally called “Discrete Event Detection Sampling,” or“DEDS,” systems and methods. A fundamental aspect of DEDS is the use ofa probability-density function (PDF) to describe the uncertaintyassociated with position attributed to any signal used to form an image.Such signals can be, for example, a detected photon or other unit ofradiation, such as particle radiation (e.g., electrons). But, DEDS isnot limited to applications involving elementary particles such asphotons or electrons; DEDS can also be used when images are formed withsignals generated in ways other than photons or particle radiation. Forexample, DEDS is applicable to methods in which discrete measurements(which can correspond to respective discrete events) are assignedrespective positions of origin and these position coordinates are usedto form an image. In these cases, application of a PDF describing theuncertainty associated with the position locations and/or the measuredvalues themselves would be useful in a manner similar to the way inwhich such data are useful when images are formed using discrete events.In a general sense, these discrete measurements are regarded as discrete“events.”

As noted, DEDS encompasses measurement of radiant events involvingphotons (PEDS) as well as radiant events involving non-photonicradiation (REDS), such as radiation of elementary particles or the likefrom a specimen. Examples of particles include, but are not limited to,electrons and alpha particles. In PEDS the photons are not limited tovisible-light photons.

In DEDS the position of origin of each detected event in or on aspecimen being imaged is convolved with a PDF related to an uncertaintyassociated with determining the position of origin of the event. ThePDFs assigned to the discrete events detected during animage-acquisition period are summed to form the image. The distributionassigned to the PDF is determined by the properties of the events and bythe characteristics of the instrumentation used to elicit and/or detectthe events.

DEDS can be implemented in both scanning and non-scanning formats. InScanning DEDS (SDEDS) the specimen to be imaged is scanned by moving thespecimen and/or a detector or detecting probe relative to each other, orby moving an interrogation beam of radiation and/or the specimenrelative to each other. During an image-acquisition period a signaldesignating the position of origin, within or on the specimen, of eachdetected discrete event is recorded and assigned an appropriate PDF. Theindividual PDFs are summed to form an image.

Certain DEDS embodiments do not require scanning the specimen withinterrogating energy (e.g., a beam of light or of electrons). TheseNon-Scanning DEDS (NSDEDS) embodiments desirably utilize detectorscomprising multiple discrete detection units that are small in sizerelative to the size of the distribution assigned to the PDF. Thus, therespective positions of the origins of the discrete events can be placedaccurately in the image. The individual events detected by eachdetection unit during an image-acquisition period are counted andassigned an appropriate PDF. In NSDEDS the position of origin of adiscrete event can be designated as the position of the individualdetection unit.

DEDS also encompasses embodiments in which discrete events arise eitherspontaneously or without the need for input of interrogating energy. Inthese embodiments the position information required for each discreteevent desirably is derived from an element(s) of the detection pathway,such as moving the specimen relative to the detectors (e.g., using scanmirrors or moving a stage on which the specimen is placed), moving adetecting probe relative to the specimen, or by using a detector withunitary detection elements of small size. The distribution used for thePDF desirably reflects the nature of the events and the properties ofthe detection pathway. In contrast, when interrogation energy is used,the distribution desirably reflects the manner in which theinterrogation energy interacted with the specimen, as well as the natureof the discrete events resulting from the interrogation.

The full advantages of DEDS are realized when a distribution that isoptimized for the properties of the specific imaging system beingutilized is used to describe the PDF applied to the position of originof each detected discrete event. The distribution describes the relativeprobability that a discrete event arose from a specified region in or onthe specimen and permits the most accurate representation, in the image,of the position of origin and the most efficient use of each event toform an image. For example, in PEDS, the distribution would be primarilydetermined by the properties of the point-spread function (PSF) of theexcitation light at its point of focus in the specimen. However, asnoted above, a number of factors may influence either the interaction ofenergy with the specimen and/or the detection of consequential discreteevents by a detector. Consequently, an optimum distribution desirably isdetermined for each type of imaging system and specimen.

DEDS can be used to form images more efficiently using scanningtechniques that are not restricted to confocal microscopy, such as NSOM(near-field scanning optical microscopy), stage-scanning, etc. DEDS canbe used for any electromagnetic radiation detected using optical ornon-optical techniques. Hence, DEDS (and PEDS) is not limited to photonsof visible light or even to photons of infrared and ultraviolet light.

The ability to converge more rapidly or with fewer discrete events andto eliminate one of the sources of error within the convergence (thelimited resolution of a pixel or voxel) is a major advantage of thesubject systems and methods. For example, the maximum likelihoodposition of two or more fluorophores separated from each other by lessthan the diffraction limit can be determined rapidly using PEDS or otherDEDS method in which the wavelength or energy of individual photons isclassified.

Probability-Density Functions

Various method embodiments as disclosed herein include obtaining, in animage-acquisition period and for each detected discrete event,respective location data and determining, from the location data,corresponding origin locations of the detected events in theimage-acquisition period. The determined origin locations are convolvedwith a probability-density function (PDF) to produce a set of imageabledata. The PDF describes the uncertainty associated with assigning aposition as the site of origin of each event. The PDF can be atwo-dimensional distribution or a three-dimensional distribution (thelatter can be abbreviated “PSF”). PSFs are useful in three-dimensionalapplications of PEDS or DEDS.

Thus, not only are PDFs used, but it is advantageous that the appliedPDFs be optimized. This involves applying an optimal PDF to individualdiscrete events, e.g., in PEDS to each photon detected. This alsoinvolves how individual PDFs applied to respective events can be summedin regions of overlap, of individual PDFs, to form an image.

With respect to applying an optimum PDF to each detected event, thedistribution used usually will depend on the instrumentation utilizedand the nature of the discrete event. As an example, for an embodimentconfigured as a laser-scanning confocal microscope (LSCM), an optimumPDF applied to each detected photon would be described primarily by theintensity distribution assumed by the excitation light at its point ofdiffraction-limited focus in or on the specimen. This is termed theexcitation point spread function (PSF_(Ex)). Typically, PSF_(Ex), can beapproximated by a Gaussian distribution having a full-width at halfmaximum (FWHM) value similar to the spatial resolution of the opticalsystem being used. By way of example, based on a Fraunhofer-diffractionapproach, a diffraction-limited PSF can be calculated in terms of afirst-order Bessel function, J₁, where the intensity profile is(2J₁(s)/s)² where s=kωD/2. Meinhart and Wereley, Meas. Sci. Technol.14:1047-1053, 2003. In this case k is the wave-number, ω is angularfrequency, and D is the diameter of the aperture. Alternatively, thePSF_(Ex) can be determined empirically for a given LSCM or other opticalsystem. The use of these distributions to describe the PDF assumes alinear relationship between the intensity of excitation radiation andthe probability of exciting production of a photon from incidence of theradiation on the specimen. For example, if fluorescent molecules havinga non-linear relationship were used in association with the specimen,then an empirically determined PDF can be used, based on the nature ofthe non-linearity involved.

Different PDFs can be used for photons or other discrete eventsoriginating from different regions of the specimen if it were shown thatthe PSF_(Ex) had different distributions in these regions. For example,this could arise due to optical aberrations present in the opticalsystem. In some cases a PSF_(Ex) can be calculated as described by Helland Stelzer, Ch. 20 in Pawley (Ed.), Handbook of Biological ConfocalMicroscopy, 2^(nd) Ed., Plenum Press, New York, 1995. Alternatively, thePSF_(Ex) of an optical system such as an LSCM can be measuredempirically as described by Rhodes et al., Optics Comm. 145:9-14, 1998,and Rhodes et al., J. Opt. Soc. Am. A 19:1689-1693, 2002. If desired,the PSF of an LSCM system or other optical system can be measured asdescribed by Hiraoka et al., Biophys. J. 57:325-333, 1990. The lattermay be used in cases in which light is emitted from a specimen in theabsence of an interrogating light source.

In the second case, summation of the PDFs applied to individual detectedevents desirably is convolved as a function of the number of eventsdetected. Again, using an LSCM system and PEDS as examples, as anincreasing number of photons are detected, photon statistics (Poissonstatistics) permit a more precise localization of the site of the originor centroid of clustered events (i.e., a structure). Thus, as moreevents are detected, the distribution used for a summed PDF will beginto narrow from that of the Gaussian based on the PSF_(Ex) used for asingle event to a narrower Gaussian. With more events being detectedfrom the same site of origin or from closely clustered sites of origin,there will be a further increase in the certainty of the locations;i.e., the ideal distribution used for a summed PDF narrows, wheretriangular waveforms provide a good approximation within a typical rangeused for fluorescent imaging, for example. Ultimately, as greaternumbers of events are detected, the summed distribution assumes a deltafunction. Importantly, this statistical implication is the basis forPEDS methods that place the precise position of individual fluorescentmolecules or of clusters of fluorescent molecules at much less than thespatial resolution dictated by the limits of diffraction. It is expectedthat localization accuracy achievable with PEDS and other DEDS methodswill be on the order of a nanometer or less, or on the order of a fewÅngstroms.

In many embodiments for PSF distributions applied to individual discreteevents determined as described above, appropriate equations are appliedto the PDF given to each event by routines in software being used toform the image, i.e., in a computer. In the case described aboveinvolving summed distributions, some flexibility can be applied to thetask of making a transition from a “standard” Gaussian distributionbased on a PSF_(Ex) applied to each detected event to an optimalsummation of these individual PDFs in regions of overlap, based on the“best” application of the particular statistical method that is used(e.g., Poisson statistics). The particular summing process used impactsthe achievable efficiency of image formation with DEDS process underdifferent conditions and with different types of specimens.

With REDS embodiments that involve non-photonic radiation, it is pointedout that elementary particles such as electrons exhibit properties ofboth particles and waves. Hence, a wave-based distribution function (aPDF) can be applied to imageable data collected using electrons. Thedata can be obtained using, for example, electron-microscopy methods,such as transmission or scanning electron microscopy. Recent innovationsin these techniques have permitted application of electron microscopytechniques to living biological specimens.

First Representative Embodiment

This embodiment is a PEDS embodiment in which an image of a specimenbeing scanned by illumination light is formed by recording the x- andy-coordinates of the position of each transmitted photon (eitherfluorescent or reflected) from the specimen that reach a detector. Thesecoordinates are obtained from position-feedback signals available fromclosed-loop scanners (e.g., galvanometers) used for scanning theillumination light. A probability-density function (PDF) is used todescribe the likelihood that a detected photon came from a region in thevicinity of its actual position.

One way to formulate and optimize the region described by the PDF is tobase the size and shape of the region on the size and shape of theillumination light at its point of focus in the specimen. The size andshape of the focused illumination light is described by the excitationpoint-spread function (PSF_(Ex)) of the optical system. See Cogswell andLarkin, Ch. 8, in Pawley (Ed.), Handbook of Biological ConfocalMicroscopy, 2^(nd) Ed., pp. 127-137, 1998. As discussed earlier above, atypical PSF assumes a more or less Gaussian distribution, and the fullwidth at half maximum (FWHM) of this distribution approximates thediffraction-limited resolution achievable with a microscope system.Although other variations are possible, in a typical application ofPEDS, the PDF assigned to the position of each detected photon is givena Gaussian distribution having an arbitrary unit amplitude and the sameFWHM value as either the measured or the calculated PSF of themicroscope system being utilized.

With reference to FIG. 1, a system 1, configured in accordance with thisembodiment, is illustrated. A light source 10, generally a laser,provides a light beam 12 to illuminate a specimen 14. Light from thebeam 12 is scanned across the specimen 14 by an x-y scanner 16. The x-yscanner 16 provides a scan pattern which may be a periodic linearlyrepetitive scan (e.g., repetitive row-by-row scan), a periodicnon-linearly repetitive scan (e.g., repetitive spiral scan), or otherscan pattern. During an image-acquisition period, the scanner 16 scansthe light beam 12 in a scan frame over a selected region of the specimen(which can be the entire specimen or a portion thereof). The term “scanframe” is used to distinguish the subject frame from an image framecomprising pixels of a sensor that are illuminated simultaneously. Inalternative embodiments, the scanner 16 is an x-y-z scanner.

The scanner 16 is driven by command signals from a drive circuit 18. Thescanner 16 can be any of various devices useful for directing light in ascan pattern. An example scanner is a galvanometer scanner that directsrotation of a mirror to direct the light beam. An x-y scanner directsthe light in first and second degrees of freedom, and to such endusually comprises two galvanometers and two mirrors. Other useful typesof scanners include, but are not limited to, piezo-actuated scanners,acousto-optical scanners, and MEMS-based scanners(micro-electromechanical systems). MEMS-based scanners employ, forexample, arrays of tip/tilt micro-mirrors. Command signals from thedrive circuit 18 include respective signals for each instantaneous pointin the scan frame; thus, the drive circuit 18 controls direction of thelight by the scanner 16 to the instantaneous points in the scan frame atthe proper respective instants in time. Not intending to be limiting, inone embodiment the scanner 16 is a non-linearly repetitive scanner asdescribed in co-pending U.S. patent application Ser. No. 10/795,205,filed Mar. 4, 2004, entitled “Method and Apparatus for Imaging UsingContinuous Non-Raster Patterns,” published as U.S. Patent ApplicationNo. 2004/0217270, on Nov. 4, 2004, both incorporated herein by referencein their entirety.

In the depicted embodiment a dichroic mirror 20 reflects the light beam12 from the scanner 16 to the specimen 14. The dichroic mirror 20 alsopasses light emitted from the specimen 14 to a detector 23. Although anyof various detectors can be used, the detector 23 in FIG. 1 is asingle-photon detector comprising, for example, a photomultiplier tube,an avalanche photo-diode, or an avalanche photo-diode array. Avalanchephoto-diode arrays reduce well-known adverse effects due to dead timeinherent in the response of an avalanche photo-diode. The distributionin space of each detected photon is approximated based on a point-spreadfunction (PSF) of the optical system embodied in the apparatus.

The drive circuit 18 produces command signals each having a respectivevalue uniquely associated with a respective position within a scan frameduring an image-acquisition period. This value may be, for example,selected from a monotonically increasing dc value as the scanner 16progresses through the scan pattern.

Whenever a photon is detected by the detector 23, the detector 23produces an output pulse 24 that is input to a discriminator 25. Fromthis input, the discriminator 25 produces a square-wave output 26 thatcomprises a clear rising edge and falling edge and that is directed to asample-and-hold circuit 28. The sample-and-hold circuit 28 can comprise,for example, an R-C (resistor-capacitor) circuit. Meanwhile, thesample-and-hold circuit 28 also receives corresponding position signalsfrom the drive circuit 18. The position signals provide, for example,potential levels to the sample-and-hold circuit 28. Thus, the signalsreceived by the sample-and-hold circuit 28 correspond to the actuallocation of the detected light, from the scanner, on or in the specimenbeing imaged. Voltage outputs from the sample-and-hold circuit 28 areconverted to corresponding digital signals by an analog-to-digitalconverter (ADC) 30. Thus, each output of the sample-and-hold circuit 28is a signal indicative of the respective position, in the scan frame, ofeach detected photon.

In this embodiment the computer 33, being programmed with routines usedfor forming an image, performs the calculations of individual PDFsapplied to the photon events. The computer 33 also performs summing ofthe PDFs.

Digital outputs from the ADC 30 may be stored in a memory (not shown) ofthe computer 33. If the scanner 16 is following its command signalsfaithfully, the current position of the scan in the scan frame at whicha photon is detected also correlates with a respective elapsed timesince the beginning of the current image-acquisition period. In otherwords, a current x-y position, or x-y-z position, of the scanner 16 hasa direct correspondence with a particular elapsed time from thebeginning of the scan. Hence, an alternative signal indicative of theposition, in the image-acquisition period, at which a photon is detectedis a scan signal corresponding to the elapsed time from the beginning ofthe image-acquisition period. If appropriate, these time moments areregistered by the computer 33. Thus, the respective time and position ofeach detected photon may be determined and registered.

The computer 33 also may be utilized to provide, from the position data,a respective time associated with each detected photon. Imprecision inthe resolution and/or sample locations may be produced during the scandue, for example, to an inability of the scanner 16 to follow itscommand signals faithfully. These imprecisions can be corrected by thecomputer using position-feedback signals from the scanner 16 (see FIG.1). The computer 33 may also be coupled to video circuitry to produce animage corresponding to these stored values of time and position. To suchend, the values are provided to a video-display driver 35 to produce theimage on a display 37. Also, using the computer 33, it is possible tooverlay the image of the scanned region with an image produced by avideo camera or the like.

The location, or site, of the origin of every detected photoncontributing to the image is determined, and the respective times atwhich the photons are detected may be recorded if desired. The locationsof the sources of individual photons are acquired with reference topositions of corresponding photons in the scan frame without, incontrast to conventional apparatus, reference to physically definedpixels. The location from which a photon was sensed is the location atwhich the scanner was directed at the moment the photon was sensed.While it can be desirable to sense every photon to obtain the maximumamount of information concerning the specimen for a given amount ofinput illumination, images can be generated in accordance withembodiments of the present invention if fewer than all photons aresensed or if groups of photons are sensed within a givenimage-acquisition period of a given scan area.

PEDS can be used for both single-photon excitation confocal imaging aswell as multi-photon excitation applications. Also, in the latterapplication, PEDS can be used with both descanned and non-descannedmodes of detection.

Second Representative Embodiment

With reference to FIG. 2, an embodiment of a method for determiningphoton location and producing an image comprises a step 50 in which anoperator places the specimen 14 in the microscope system 1. In the step52, scanning of the light beam 12 over the specimen 14 is initiated.Respective photon locations are recorded (54) if and when photons aredetected by the single-photon detector 23. A display of positioninformation 56 may then be provided at the display 37. If a “scanperiod” (image-acquisition period) is not complete 58, operationcontinues, and detected photons will again have their respectivelocations recorded 54. After the scan period, operation proceeds forfurther data processing, including a decision (58) as to whether thescan period is ended or not.

If the scan period has ended, display parameters, e.g., rasterlocations, are selected 60 to provide a framework so that recordedphoton locations in non-raster space can be mapped into raster images onthe display 37. Display parameters can include a grey or color-basedscale for displaying density functions. Mapping is advantageous sincethe recorded data typically has a finer resolution than the pixelswithin the raster. In other embodiments, in which scans are also made atsuccessive depths in the specimen 14, a set of sample data can be mappedinto three-dimensional voxel space. Respective probability-densityfunctions (PDFs) are accumulated (summed) 62. The PDFs may be summed by,for example, a distributive or an associative method. In the associativemethod, an intensity value is calculated based on distances to a numbern of nearest photons for each pixel. In the distributive method, eachphoton record is accessed and mapped into one or more raster locations.In this method, both the x- and y-locations can be sampled to a highdegree of precision. Therefore, the respective PDF of a single photon inone display pixel can make fractional contributions to one or more otherpixels. In one embodiment, the locations are sampled with 12-bitresolution. This level of resolution on one axis yields atwo-dimensional image resolution of 2¹²×2¹²=16 megapixels. This level ofimage resolution may be described as a 16-megapixel raster space. Theaccumulation of photon-density functions continues until processing ofan image of the scan is completed 64. Another scan may be initiated 66,or the operation may be completed.

FIGS. 3 and 4 are illustrations of sensed photons and their associatedPDFs. FIG. 3 consists of FIGS. 3( a) and 3(b). In FIG. 3( a) solidcircles represent respective single photons that have been detected andthat have had their respective positions determined by one degree offreedom. Associated with each photon is a PDF. The horizontal extent ofFIG. 3( a) defines a region that could, for example, correspond to adisplay pixel. Summing these PDFs yields the solid curve in FIG. 3( b).Summing of photon PDFs causes the solid curve to converge to an idealdistribution curve represented by the dashed curve. This summing of PDFsrequires fewer photons to converge to the ideal density distributionassociated with an image feature than are required using conventionalphoton binning. As a result, certain embodiments permit images to beformed more efficiently than by other embodiments or than conventionaldevices.

FIG. 4 consists of FIGS. 4( a) and 4(b). In FIG. 4( a), solid circlesrepresent photons that have been detected and that are associated withan image feature. FIG. 4( b) represents a summation of the PDFs of thepositions of the photons of FIG. 4( a). The center of the curve in FIG.4( b), indicated by an arrow, represents the central location of theimage feature as determined from the summation. The resolution of thecentral position obtained in this statistical manner is less than thediffraction limit of light (0.6λ/NA). This physical limit is thusovercome by certain embodiments of the present invention.

Third Representative Embodiment

FIG. 5 is an illustration of data collected in an embodiment in whichtime intervals between pulses are measured to determine locations ofcorresponding photons. Data may be collected using, for example, theapparatus of FIG. 1. However, rather than having the sample-and-holdcircuit 28 store a potential level in response to each square wave 26, apulse output indicating time of production of the square wave 26 isproduced. The apparatus of also produces periodic “milepost” pulseshaving constant inter-pulse intervals. The milepost pulses can beproduced by, for example, a clock or a constant-frequency oscillator.Each milepost pulse corresponds to a known position of a scanning beamin the scan pattern of the scanner 16.

In FIG. 5 the horizontal axis represents time. The curve plotted in x-ycoordinates indicates the path of the scanning beam. In the presentexample, the scanning pattern comprises a spiral path. See U.S. PatentApplication No. 2004/0217270, published on Nov. 4, 2004, incorporatedherein by reference in its entirety. The solid dots represent respectivelocations from which single photons are received, and the circlessurrounding each dot represent the point-spread function inherent in theoptical system of the confocal microscope system 1. The squaresrepresent milepost beam locations. Each point in time during a scan hasa unique corresponding x-y position. The position of the scan at theinstant of each milestone pulse is known. In the present example, photondetection pulses are produced, for example, after intervals I₀, I₁, I₂,I₃, and I₄. The computer 33 performs linear interpolation to determinethe respective location of each detected photon. In this example,interpolation is performed between the times of the consecutive milepostbeam locations flanking a particular interval. Interpolations can alsobe performed between other pairs of milepost beam locations flanking anyof the intervals I₀, I₁, I₂, I₃, and I₄. In another alternativeconfiguration, a plurality of interpolations may be performedrespectively between each of multiple pairs of beam mileposts. Theresults of the interpolations can be averaged or otherwise processed.Based on PDFs, an estimate of the spatial distribution is made togenerate images as described above.

Certain embodiments can thus provide for measurement of the actuallocations of detected photons. Once the locations are measured, precisevalues indicative of the locations can be stored. A stored set oflocation data in time and space is thus provided for later recall andfurther processing, if desired. Hence, it is not necessary to repeat anexperiment to use different measurement parameters with the data.Locations can be determined to a far greater degree of precision than isavailable in currently available display techniques. The precision isnot limited by the physical diffraction limit inherent in opticalmeasurements because image frames are constructed by summing photonPDFs. This requires fewer photons to converge to an ideal densitydistribution associated with a feature image than are required usingconventional pixel binning. The resulting increased sensitivityexhibited by embodiments of the present invention permits reduction orelimination of adverse effects of over-illumination of specimens.

Devices, such as a quad-cell photodetector, capacitance (eddy-current)sensor, or the like, can be used to improve the accuracy and precisionof assigning respective positions to the photons. Mechanical accuracy isnot limited by any of sort of diffraction limit or other foundationallimit down to molecular scales and, as such, can be measured accuratelyin a number of different ways.

The data obtained as described above may be processed in a number ofdifferent ways. For example, the data can be rendered in a histogramformat for commonly used analyses, such as fluorescence-correlationspectroscopy. Alternatively, an interval clock, relative to the timingof a pulsed laser, can be triggered by photon detection during dataacquisition, and fluorescence lifetimes can be analyzed. In anothervariation, detected photons can be categorized according to their energycontent and assigned an appropriate distinguishing color. In addition,it is possible to temporally expand and/or contract a data set acquiredduring a single high-speed acquisition period. Consequently, flexibilityis provided in extracting kinetic information concerning the dynamics ofthe process being imaged over any relevant time scale.

In some embodiments, repeated scans of a specimen allow for comparisonof one scan to another, and corresponding elements of one scan toanother. The scans may be consecutive or non-consecutive, and theelements may be images, portions of images, or photons or sets ofphotons. Alternatively, positions of photons measured over integratedgroups of image-acquisition periods may be compared. With appropriatecompensation for noise and thermal expansion, movements in thesub-nanometer range may be detected.

Once a data set of positions of origins of photons has been acquired,the set can be used to cast the data in any time frame or to applydifferent PDFs, etc., as desired. Thus, the data set can be manipulatedin a wide a manner as other types of data sets, especially with theavailability of a many types of computers and computer software.

Another use of the photon-detection data is to produce an image on adisplay or the like. Photon-position data is determined to a high degreeof resolution and stored (e.g., in memory of the computer). To produce adisplay of the data, the recorded positions of photons may be mappedinto the raster space of a display device. FIG. 6, consisting of FIGS.6( a), 6(b), and 6(c), is useful in understanding embodiments of onemethod for mapping. FIG. 6( a) represents a non-raster scan (NRS)pattern, FIG. 6( b) depicts a “distributive” method of mapping, and FIG.6( c) depicts an “associative” method of mapping.

With regard to the distributive method (FIG. 6( b)), “n” nearesttwo-dimensional raster display pixels are considered as pixels to whichone photon scan location can be assigned. As in the associative methoddescribed below, the influence of each newly acquired sample on nearbyraster pixels can be weighted to the distance between the location ofthe sample point and the location of the display pixel (e.g., inverselyproportional to produce linear interpolation). In addition, the timesince a pixel was last updated can be taken into account. Raster (i.e.,grid) locations in the track of a spiral scan pattern (or other scanpattern) are assigned sampled-intensity values and weight factors. Onesuitable weight factor is inversely proportional to the distance fromthe actual scan path. Other functions of distance alternatively can beused. Raster-intensity values are then assigned based on theintensities/weights at each location or interpolated from neighboringpixels if no weights/intensities have been stored (a situationillustrated as white grids above). An advantage of this scheme is thatmost of the computation required for producing raster images can beperformed one point at a time, as each sample is acquired. Thedistributive method usually requires more computational time and isbetter suited for producing a final raster-display image, once acomplete non-raster sample set has been acquired.

In the associative method (FIG. 6( c)), the “n” nearest sampled (i.e.,non-raster) points to each two-dimensional (raster) display pixel arefound. By weighting non-raster sample points inversely proportionally tothe distance between the location of the sample point and the locationof the raster display pixel, it is possible to generate an accuraterepresentation of non-raster data rapidly with smooth transitions in theraster-grid display. Each raster pixel is assigned a value based on anaverage intensity that is weighted. A weighting factor may be inverselyproportional to the distance between the raster location and the spiralsample location. Other functions of distance can be used. In thisexample showing how the intensity values of two pixel locations (pointedto by the collection of arrows) are computed, three nearest spiralsamples are used to make the calculation. In both schemes illustrated inFIGS. 6( b) and 6(c), relative weight factors are represented asgrayscale intensity, where darker locations are weighted more heavily.

A significant advantage that can be achieved with either mapping methodis that the number of non-raster samples can be independent of thenumber of raster-display pixels. Thus, if high temporal resolution(i.e., a high frame-rate) is desired, a small number of samples along anon-raster pattern can produce a roughly uniform distribution of samplesalong a raster or non-raster pattern. On the other hand, if high spatialresolution is desired, then more “spirals” can be selected. Whentracking rapid dynamic behaviors or making comparisons withspatial-temporal mathematical models, the non-raster pattern can be usedto select just enough spatial resolution while maximizing temporalresolution. The number of command points per image and frame rate can bechosen under software control to be any values on a continuous scale(i.e., points can be added or subtracted). Maximum values are governedonly by sinusoidal scanning frequency and photon-detection efficiencies,not by the characteristics of display devices.

As an example of using a non-raster pattern with a NRS-LSCM, if eachsample required a dwell time of 0.5 microseconds to gather a sufficientnumber of photons and if 2000 samples were needed for adequate spatialresolution, then a frame-rate of 0.5×2000=1000 frames/second could beachieved. Greater frame-acquisition rates can be chosen, under softwarecontrol, without having to make any modifications to hardware. In theseexamples, a low number of spiral samples (e.g., 450 points along aspiral scan frame) in combination with a low ratio of spiral sample toraster pixel have intentionally been used to simplify illustration ofthe different mapping methods.

If desired, the highest possible scan rates can be used withoutconsideration of the number of photons being acquired. After a completedata set has been acquired, raster-space images having desired intensityvalues can be constructed by combining one or more scan frames. Thus,using a single data set, a dynamic event can either be viewed to observechanges occurring over time by comparing respective images formed fromsequential sample frames, or the event can be viewed statically ondifferent time scales by combining data from more than one sample frame.In the latter case, the accuracy of parameters obtained for a dynamicevent described at high temporal resolution by one or a few scan framescan be compared with those derived from images of the same eventobtained over a longer interval. Useful information can thus be providedregarding the interval of scanning needed to obtain a given level ofaccuracy.

Storing of the data thus obtained allows for further use of the data.Frame images can be reconstructed and viewed at different temporalrates, thereby permitting compression or expansion of viewing of anoverall data set. The availability of complete data sets in space andtime makes it possible to conduct repeated post-hoc analyses rather thanrepeating an experiment using different measurement parameters. Thissaves cost and reduces inconvenience. Availability of post-hoc analysisguarantees that analysis may be made even when a specimen is no longeravailable or is no longer responsive to radiation excitation. Thisfeature provides a number of advantages including the ability to: (i)compare conventional images using pixel “bins” with those accumulatedusing DEDS-based PDFs, and (ii) determine the exact sequence of photonicresponses relative to other events. For example, a photon event can berelated to an electronic or metabolic change in the specimen beingimaged.

Another use of REDS/PEDS is to overcome prior-art limitations ofscanning microscopes in achieving required spatial resolution and detailin producing an image of a biological specimen or inspecting propertiesof the surface of a material. Using prior-art scanning-microscopetechniques usually involves the need to utilize microscope objectives,having high numerical aperture (NA), that require immersion in a fluidmedium and that must be situated in close apposition to the specimen orsurface to produce required spatial resolution and detail. To minimizespecimen manipulation and increase throughput, however, it isadvantageous to utilize lower-NA objectives having longer workingdistances that allow an air interface between the objective and thespecimen or surface.

Fourth Representative Embodiment

This embodiment is similar in some respects to that of the firstrepresentative embodiment but does not involve a scanning orinterrogating beam. This embodiment is illustrated in FIG. 7, in whichcomponents similar to those shown in FIG. 1 have the same respectivereference numerals and are not described further.

The specimen 14 is positioned on a stage 110 or the like that isconfigured for motion in the x and y directions. X- and y-positioncontrol is provided by the computer 33. To such end, digital controlsignals from the computer 33 are converted to corresponding analogsignals by a digital-to-analog converter (DAC) 112. The resulting analogsignals for x- and y-position control are converted to correspondingstage-drive signals by drive circuitry 114. X- and y-position detectionof the stage 110 is performed by position-sense circuitry 116 (e.g.,encoders or interferometers), which provides x- and y-position feedbackto the sample-and-hold circuit 28. For optimal detection of radiantevents occurring on or in the specimen 14, the z-position of the stage110 is controlled by a focus control 118 that receives appropriatecontrol signals from the computer 33. Actual detection of radiant eventsis performed by at least one “single-event detector” 120, which routescorresponding detection pulses 24 to the discriminator circuit 25. Thediscriminator circuit 25 converts the detection pulses 24 tocorresponding square-wave pulses 26 that are routed to thesample-and-hold circuit 28. Output from the sample-and-hold circuit 28is converted to corresponding digital data by the ADC 30 and routed tothe computer 33. In addition to its various computational tasks, thecomputer 33 also convolves PDFs to the data delivered from the ADC 30and sums the PDFs to produce imageable data. The imageable data arerouted to a display driver 35 and then to a display 37.

EXAMPLES Example 1

This example is directed to the measurement of the release of calciumion, Ca²⁺, from intracellular sarcoplasmic reticulum (SR) stores incardiac cells using an apparatus as disclosed above. Ca²⁺-releaseactivates contractions of the heart for pumping blood throughout thebody. Ca²⁺ is released through ryanodine receptor (RyR) Ca²⁺ channelspresent in SR membranes. Information concerning the functionalproperties of these channels, as they exist inside heart cells, can helpin understanding how contraction of the heart is activated andregulated. Since RyR channels are present in intracellular membranes,they cannot be studied using conventional microelectrode-basedelectrophysiological techniques. However, changes in intracellular Ca²⁺can be measured non-invasively by monitoring fluorescence of dyes, suchas fluo-3, introduced into the cytoplasm of the cell. Fluorescenceincreases when Ca²⁺ binds to the dye.

Small increases in fluo-3 fluorescence observed in cardiac cells, termed“Ca²⁺ sparks,” are thought to be due to release of Ca²⁺ from a smallnumber of RyR channels. A “Ca²⁺ spark” represents a photon emitted by acalcium-sensitive fluorescent dye excited by a laser beam in thepresence of calcium ions. Ca²⁺ sparks may represent elemental eventsthat are first steps in the activation of contractions in the heart. Assuch, they can provide information concerning the activity andproperties of RyR channels in intact cardiac cells. A situation thatcomplicates relating the properties of Ca²⁺ sparks directly to activityof RyR channels is that spark properties can be influenced by conditionsand factors within heart cells that are not related to the activity ofRyR channels. These factors interact with one another and cannot beeasily manipulated individually in intact cells. Thus, it has provendifficult to assess in a direct experimental manner how each factor andcondition alters Ca²⁺-spark properties. To date, workers in the fieldhave attempted to use computer modeling and simulations to dissectinfluences by cellular factors and conditions from those related to theactivity of RyR channels.

An alternative and complementary approach to this problem is an in vitrooptical-bilayer system that permits imaging of fluo-3 fluorescence inresponse to Ca²⁺ flux through single RyR channels reconstituted intoartificial planar lipid-bilayer membranes simultaneously with electricalrecording of single RyR-channel Ca²⁺ currents. PEDS is advantageous forsolving this because PEDS excels at permitting signals with low spatialfrequencies to be imaged over small scan ranges in a more efficientmanner.

Example 2

This example is of the system 1 of FIG. 1, configured as a confocalmicroscope. The microscope comprised a model MRC 600 laser-scanningconfocal-microscope system (LSCM) from BioRad Laboratories, Hercules,Calif. The laser 10 was any of various ion-lasers or solid-state lasersemitting in the ultraviolet to infrared wavelengths. Examples areavailable from Melles Griot of Rochester, N.Y., and Blue Sky Research ofMilpitas, Calif. The scanner 16 comprised an x-y steering device,including mirrors mounted on closed-loop galvanometers, available fromCambridge Technology, Inc., of Cambridge, Mass. A pair of CambridgeTechnology Model 6800 closed-loop galvanometers was used, which canexhibit scan frequencies of 500-600 Hz over mechanical scan angles of≦10°. These frequencies were determined for raster scanning (i.e.,repeatedly starting and stopping). Scan frequencies of slightly greaterthan 1 kHz (limited by safeguard circuitry on the driver card) can beobtained using non-raster scanning and position-feedback signals toestablish sample position in non-raster space.

The dichroic mirror 20 was obtained from Semrock, Inc., of Rochester,N.Y. The laser beam was focused onto a specimen or sample by a focusingdevice such as a microscope objective.

Movements of the beam-steering device and scanning of the radiation weredictated by command signals originating from a computer under softwarecontrol and converted to appropriate analog voltages by adigital-to-analog converter (DAC). The DAC had a resolution dictated bythe spatial-resolution requirements of the measurement being made, andwas obtained from National Instruments, Austin, Tex. The beam-steeringdevice was moved in either a raster pattern or in a non-raster patternto scan the electromagnetic radiation across the specimen or sample.Photons, due to reflected or fluorescent light and originating from afocal plane in the specimen or sample, passed through thewavelength-selective device and were counted as single events by asingle-event detector, in this example an avalanche photodiode obtainedfrom Perkin Elmer Optoelectronics of Wellesley, Mass. Alternatively, aphotomultiplier tube available from Hamamatsu Corporation ofBridgewater, N.J., operating in a single-photon-counting mode can beused. Single pulses were sent from the detector to a discriminatorcircuit for every photon detected.

The BioRad 600 LSCM can scan a single line in the x-dimension in ˜2msec. Therefore a full-frame x-y image containing 768×512 pixels (i.e.,512 t-line scans, with each line containing 768 pixels) could beobtained in ˜1 sec. The rise-time of a Ca²⁺ spark in a cardiac cell is˜8-12 msec. Consequently, using this system, only six points or lesscould be used to describe the onset of the spark event. Single-x, t-linescans were employed to achieve the highest scan-rates possible. In thisapproach, spatial sampling was collapsed to a single dimension, as thesame line is scanned repeatedly as rapidly as possible.

Since Ca²⁺ sparks are four-dimensional events occurring in x, y, and zspatial dimensions, as well as in time. Hence, spatial sampling and datainterpretation sometimes were not optimal.

One reason for the limited temporal resolution of the MRC 600 in someLSCM systems is that mirrors mounted on separate closed-loopgalvanometers (CLGs) are used to scan the laser beam in the x- andy-dimensions in a raster pattern. This requires that the laser beam beturned around at the beginning and end of each line, which involvesstopping and starting a CLG. Since the shaft of a CLG has significantmass, and since relatively large mirrors are typically used toaccommodate laser beams whose diameters have been expanded for opticalreasons, considerable inertia is involved. The time required to reversethe direction of the laser beam is a significant portion of the timerequired to scan a single line, which imposes a fundamental limit on thescan rates that can be achieved. In addition, since pixel size incurrent LSCM systems is determined by the pixel clock interval, uniformsampling during a scan requires that the laser beam move at a constantvelocity. Thus, the time required for the CLG to accelerate to aconstant velocity can also impact scanning capabilities.

Example 3

In this example the discriminator circuit (see item 25 in FIG. 1) wasadjusted to separate pulses caused by photons from those caused byrandom noise. Each pulse generated by a photon resulted in a digitalpulse being sent to the sample-and-hold circuit (see item 28 in FIG. 1).Each time a digital pulse was received, a corresponding set of voltagesrepresenting the x- and y-positions of the beam-steering device at thetime the photon was detected were retained by the sample-and-holdcircuit. The position signals from the beam-steering device wereconverted to digital signals and passed to the computer (item 33 inFIG. 1) by the analog-to-digital converter (ADC, item 30 in FIG. 1)having a resolution appropriate for the measurement being made.

The ADC was obtained from National Instruments, Austin, Tex. Theposition of each photon detected within the image domain was transmittedvia a display driver (item 35 in FIG. 1) to a display device, such as acomputer monitor, to form an image of the illuminated region of thespecimen or sample. The display utilized either a raster or non-rasterscanning format.

The intensity value assigned to each photon in the spatial domain of theimage could be adjusted as a probability-density function (PDF)formulated relative to the point-spread function (PSF) of theilluminating radiation and the probability of exciting emission from theexcitation properties of a fluorophore positioned within theillumination PSF. The focal plane in the specimen or sample beingilluminated by the electromagnetic radiation was selected under computercontrol via focus-control circuitry controlling the position in thez-axis at which the radiation is focused in the specimen or sample.(This control is currently typically implemented via a serial (USB) portinterface with the focus-control circuitry.) As is the case with x- andy-position signals, voltage-indicated z-positions could also be passedvia an ADC channel to the sample-and-hold circuit 28 and then to thecomputer 33. Algorithms commonly used to eliminate photons originatingfrom above and below the focal plane can be used to enhance imagesobtained in this example.

The NRS-LSCM of this example offered particular advantages for imagingdynamic processes. Such dynamic processes include changes inintracellular Ca²⁺ (Ca²⁺ sparks and waves) involved in tissue activationand intracellular signaling, changes in membrane potential in excitabletissues (e.g., heart and brain), and the spread of activation within theGI tract. Images of these events, as well as of many other cellularprocesses, contain relatively low spatial frequencies. Therefore,relatively low sampling frequencies (and consequently high scan rates)can be used to establish their properties in an adequate manner. Thisexample and other embodiments of the present invention can image eventsinvolving intermediate to low spatial frequencies at maximal possible(photon-limited) sampling rates. Because spatial-resolution capabilitiesare not sacrificed to obtain greater temporal resolution, the NRS-LSCMsystem provides a data-collection rate equal to the performance ofsystems for imaging specimens containing high spatial frequencies, wheregreater sampling rates (and lower scan speeds) are used.

Further examples below show that DEDS permits approximation of the truedistribution of photons or other discrete events arising from a specimenmore efficiently and with fewer photons than achieved using conventionalpixel-based binning methods. This results, at least in part, from anincrease in the signal-to-noise ratio (S/N ratio or SNR) of the imageobtainable using DEDS. Two SNR values are commonly measured. An SNRvalue can be defined as the ratio of the signal, measured as the meannumber of photons arising from the specimen (signal_(spec)) and thenoise (standard deviation of the mean signal) present either in thesignal obtained from the specimen (noise_(spec)) or in the signalobtained from a background (bkg) region not occupied by the specimen(noise_(bkg)). To compare the effects of DEDS and binning on both typesof SNR, photon-event files were generated that contain the x- andy-position coordinates of each photon detected during an image frame.

Example 4

To permit direct comparison, PEDS and conventional binning processeswere used in this example to form images from the same photon-eventfile. To assess conventional binning, a consensus optimal pixel size(FWHM of the PSF/2.3) was utilized. See Pawley, Chapter 4 of Pawley(Ed.), Handbook of Biological Confocal Microscopy, 3^(rd) Ed., pp.59-79, 2006. A 60×oil-immersion objective having an NA of 1.45 was usedto obtain images. A FWHM of 202 nm was calculated from the formula:0.6λ/NA (where λ=488 nm, the excitation light wavelength). This yieldedan optimal square pixel size with a lateral dimension of 88 nm. The areascanned in the specimen to generate the photon-event file was fit withan array of 88-nm pixels having an equal number of rows and columns. Thenumber of photons present within each pixel was summed. The summedvalues were then used as intensity values to form an image.

For evaluation of PEDS, a PDF was applied to each photon position in thephoton-event file. In this example the PDF was a Gaussian distribution,in which the area under the curve represents unity, the value given adiscrete event prior to assignment of a PDF, so that the intensityrepresented by a single discrete event is not altered. The Gaussiandistribution had an arbitrary unit amplitude of which the FWHM was equalto the 202-nm FWHM of the calculated PSF. Individual PDF values weresummed in regions of overlap. The resulting values were used asintensity values to form an image. As previously discussed, in PEDSpixels per se are not used to generate an image. However, due to thenature of currently available display devices (e.g., computer monitors),pixels are involved in displaying an image for viewing.

The two types of SNR, namely signal_(spec)/noise_(bkg) andsignal_(spec)/noise_(spec), were measured. Fluorescently labeledpolystyrene beads of 1.9 μm diameter were used to measuresignal_(spec)/noise_(bkg) values. These beads were selected because alarge number of image frames could be collected without significantphoto-bleaching. The second type of SNR, namelysignal_(spec)/noise_(spec), was measured using a uniformly fluorescentslide or a uniformly reflective tungsten-coated silicon substrate. Hibbset al., Ch. 36 in Pawley (Ed.), Handbook of Biological ConfocalMicroscopy, 3^(rd) Ed., pp. 650-671, 2006. In both cases, photon-eventfiles having an increasing number of detected photons were collected andimaged using both the PEDS and binning processes.

The results obtained are shown in FIGS. 8 and 9. FIG. 8 is a scatterplot of SNR (signal_(spec)/noise_(bkg)) values (ordinate) measured forimages formed from the same photon-event files using either PEDS (darkdiamonds) or conventional binning (lighter squares). Uniformlyfluorescent, 1.9-μm diameter polystyrene beads were imaged usingincreasing excitation-light intensities to produce a wide range ofphoton counts (abscissa) in a region of interest (ROI) placed within theboundaries of the bead and used to collect the specimen signal values.Background noise values were obtained as the standard deviation of themean photon-flux signal in a ROI of identical size placed sufficientlydistant from the bead so that the recorded values were not influenced byphotons coming from fluorophores in the bead. FIG. 9 is a scatter plotof SNR (signal_(spec)/noise_(spec)) values (ordinate) measured forimages formed from the same photon-event files using either PEDS (darkdiamonds) or conventional binning (lighter squares). A uniformreflective surface consisting of tungsten deposited on silicon wasimaged using increasing excitation-light intensities to produce a widerange of photon counts (abscissa) in a region of interest (ROI) placedin the center of the image and used to define the area from which boththe specimen signal and specimen signal noise (standard deviation ofmean specimen signal values) values were measured. Individual values areindicated by the symbols, while the lines represent a power function fitto these values. Similar results were obtained when a uniformlyfluorescent plastic slide was used as a specimen.

In each case, SNR values in PEDS images exceeded those in conventionalbinning images by factors of 4 to 6. Due to the nature of therelationships involved, large differences in the intensities of theillumination light produced similar SNR values using PEDS and binningunder different imaging conditions.

Example 5

The results in Example 4 show that images can be formed more efficientlywith PEDS, or alternatively that PEDS requires fewer photons to form animage comparable to that obtained with a greater number of photons withbinning. In the current example, two studies were conducted to assessthe practical significance of this. First, the extent to which 500-nmfluorescent polystyrene beads photo-bleached during a 30-minute periodof continuous laser illumination when images were formed with eitherPEDS or binning process was assessed. This involved the use of a ±0.2volt galvanometer signal range. In a second study, actin filaments in afibroblast cell were imaged. These images required a greater scannedarea and a galvanometer signal range of ±2.0 volts. In both cases, anillumination-light intensity typical of that employed in commerciallyavailable laser scanning confocal microscope systems was used to obtainSNR values typical of those obtained by binning. The excitationintensity of the laser was then adjusted to obtain a SNR value for PEDSthat was similar or up to 2× greater than that resulting from binning.

Results from the second test, which involved imaging actin filaments inchemically preserved cells, are shown in FIG. 10. In this studyphoton-event files were obtained from the same specimen region usingthree different illumination-light intensities. Images from the threephoton-event files were then formed using either PEDS or binning.Although evaluation of the detail discernable in complex images such asthese is subjective and dependent on the objective of the experiment,SNR, signal_(spec)/noise_(bkg), values are provided. These imagesdemonstrate that comparable image detail can be obtained with PEDS using5-10 times lower excitation-light intensities than required withbinning.

Specifically, FIG. 10 shows images of actin fibers stained withphalloidin labeled with Alexa-488 obtained from the same cell region.The photon-event files used to generate the images shown in images 1-3in each row were obtained at laser illumination-light intensities (I) of8.3, 1.9, and 0.9 microwatts. Images in the top and bottom rows wereformed using binning and PEDS, respectively. The SNR(signal_(spec)/noise_(bkg)) values obtained for each image are shown inthe bottom left corner of each image, as a quantitative measure of imagequality. Illumination intensities were adjusted in each case from aninitial level typical of that used routinely in a commercially availablelaser scanning confocal system to result in approximately a 2-foldreduction in the SNR associated with each series of images.

Technical limitations may also exist, wherein use of more efficient(e.g., 16-bit) ADCs and position-feedback signals having greaterpositional resolution likely increase PEDS efficiencies in theseapplications relative to binning as scanned areas are increased. Therelationship between the size of the scanned region and the positionalresolution of this PEDS example suggests that the magnification factorof the objective used has an impact on image-formation. For example,100× and 60× objectives both having NA=1.45 should result in the samediffraction-limited spatial resolution in an image. However, the 100×objective should result in a greater positional resolution with PEDS andpermit an image to be formed more efficiently than with the 60×objective.

The ability, using PEDS (as an example DEDS method), to form images fromfewer detected photons has several consequences. First, images havingSNR values comparable or superior to those obtained with binning can beobtained at the same scanning rates with PEDS using reducedexcitation-light intensities. When fluorescent light is being imaged,photo-bleaching of fluorophores present in the specimen (living orpreserved) and associated photo-toxicity in living specimens can beproblematic and limit the number of images that can be obtained. Sincephoto-bleaching and photo-toxicity increase as the intensity of theillumination light is increased, the use of PEDS results in a decreasedincidence of both events. Thus, specimens can be imaged for longerperiods of time. Second, if necessary, the use of PEDS would also permita greater number of image frames to be averaged to decrease image SNRvalues to even greater extents. Third, if similar excitation-lightintensities are used, images with comparable SNR values can be obtainedusing faster scan rates with PEDS than with binning. Fourth, since fewerphotons are required to form images having comparable SNR values usingPEDS, the size of the pinhole aperture placed in front of the detectorin a scanning confocal microscope system can be reduced to produceoptical-image sections having less out-of-focus light in the z-axis thancan be achieved using binning. Fifth, other than using a detector suchas a photomultiplier or avalanche photodiode, in a photon-counting modeand the ability to trigger the acquisition of photon x, y positioncoordinates, no other complexities in the optical system are requiredwith PEDS. Photon counting has long been recognized to be superior inperformance to integrating detected photon events as analog signals.

In the embodiments described above, the scan format is a type ofnon-raster scan identified as a spiral scan. Other scan formatsalternatively may be utilized, including other raster and non-rasterscan formats.

As illustrated by the foregoing results, advantages of DEDS areincreased SNR and all accompanying consequences, including (but notlimited to): (a) fewer detected events are required to form images; (b)images can be obtained either more rapidly using a given intensity ofexcitation energy or with lower excitation-energy intensities withlonger illumination intervals; (c) fluorescent images can be obtained ofboth live and preserved specimens, with less photo-bleaching and/orother photo-toxicity; and (d) images of live specimens can be obtainedfor longer periods of time with reduced levels of photo-toxicity. Theability to form images more efficiently is of particular importance in,for example, genetic-screening applications, such as micro-arrayanalysis and chromosome labeling, where low numbers of fluorescentmolecules are present and a reduced number of photons is available fordetection.

It is to be understood that the foregoing is a description of preferredand other embodiments. The foregoing description therefore is not to beconstrued as itself limiting of the scope of the invention.

1. A method for producing a set of imageable data on discrete eventsassociated with a specimen, comprising: detecting the discrete eventsoccurring during an image-acquisition period; obtaining respectivelocation data for the detected events, the location data correspondingto respective sites of origin of the detected events in or on thespecimen; assigning to the location data, for each relevant detectedevent, a distribution determined by a probability-density function (PDF)to produce a set of imageable data.
 2. The method of claim 1, whereinthe discrete events are respective radiant events.
 3. The method ofclaim 2, wherein each radiant event involves at least one respectivephoton.
 4. The method of claim 2, wherein the radiant events involve atleast one of transmission, reflection, fluorescence, andchemiluminescence.
 5. The method of claim 1, further comprising: summingthe imageable data; and displaying an image of the summed data.
 6. Themethod of claim 1, further comprising: storing the imageable data in amemory; recalling the data from the memory; and processing the recalleddata to form, from the data, an image of the discrete events.
 7. Themethod of claim 6, wherein processing the data comprises: processing afirst set of imageable data obtained in a first unit of sampling time;processing a second set of imageable data obtained in a second unit ofsampling time; comparing the first and second sets of processed data;and displaying a result of the comparison.
 8. The method of claim 1,further comprising exposing the specimen to a discrete-event stimulus toproduce the discrete events on or in the specimen.
 9. The method ofclaim 1, wherein the discrete-event stimulus is a laser beam.
 10. Themethod of claim 1, wherein the location data comprise correspondingtemporal data pertaining to respective times of the detected events froma beginning of the image-acquisition period.
 11. The method of claim 1,wherein: the discrete events comprise respective photons propagatingfrom the specimen; and the photons are detected using a photon detector.12. The method of claim 1, wherein: obtaining the respective locationdata comprises scanning involving moving the specimen, in a scanpattern, relative to the detector; and monitoring specimen position inthe scan pattern.
 13. The method of claim 1, wherein: obtaining therespective location data comprises scanning involving moving thedetector, in a scan pattern, relative to the specimen; and monitoringdetector position in the scan pattern.
 14. The method of claim 1,wherein: obtaining the respective location data comprises scanninginvolving moving an energy beam, in a scan pattern, relative to thespecimen as the energy beam is incident to the specimen; and monitoringbeam position in the scan pattern.
 15. A method for producing an imageof at least a region of interest of a specimen, comprising: detectingdiscrete events occurring on or in the region of interest; in animage-acquisition period and for each detected discrete event, obtainingcorresponding location data; determining, from the location data,corresponding origin locations of the detected events; selecting aprobability-density function (PDF); convolving each of the determinedorigin locations with the PDF; summing the PDF data over theimage-acquisition period; processing the summed PDF data for display;and displaying the processed data as an image.
 16. The method of claim15, wherein the discrete events are respective photon events.
 17. Themethod of claim 16, further comprising passing photons from photonevents occurring on or in the specimen through a microscope opticalsystem to a photon detector.
 18. The method of claim 15, wherein the PDFis calculated or determined empirically, based on instrumentation usedfor performing the method, properties of the specimen, and nature of thediscrete events.
 19. A system for producing data pertaining to discreteevents occurring on or in a region of interest of a specimen,comprising: a discrete-event detector that is positionable relative tothe region of interest to detect discrete events occurring in the regionof interest; a location-determining device associated with the detectorand configured to determine respective locations of detected discreteevents in the region of interest; and a computer connected to thedetector and location-determining device, the computer being programmedto convolve the determined locations with a probability-density function(PDF) and to correlate the summed PDFs with the determined locations.20. The system of claim 19, wherein: the computer is further configuredto sum the PDFs in the image-acquisition period; and the system furthercomprises a display driver connected to the computer and a displayconnected to the display driver.
 21. The system of claim 19, wherein:the discrete events comprise photons; the discrete-event detectorcomprises a photon detector; and the system further comprises an opticalsystem situated between the photon detector and the region of interest.22. A system for imaging a specimen, comprising: a radiant-eventdetector placed relative to the specimen: a scanner comprising alocation-determining device; a scanner driver connected to the scannerto drive the scanner to any of multiple positions in a scan pattern in aregion of interest of the specimen; a location sensor configured, forradiant events detected by the detector, to determine correspondinglocations in the scan pattern; a computer connected to the detector,scanner driver, and location sensor, the computer being configured toconvolve each detected location with a probability-density function(PDF) and to sum the PDFs; and a display connected to the computer toreceive the summed PDFs from the computer.
 23. The system of claim 22,further comprising a radiant-event stimulator, wherein the scanner iscoupled to the radiant-event stimulator and configured to move theradiant-event stimulator over the scan pattern.
 24. The system of claim23, wherein the radiant-event stimulator is a laser beam.
 25. A methodfor generating image data, comprising: scanning a specimen during animage-acquisition period over a scan pattern comprising a plurality ofscan positions; detecting discrete events produced on or in the specimenduring the image-acquisition period; detecting respective locationsassociated with the discrete events in the scan pattern; selecting atleast one probability-density function (PDF); applying the at least onePDF to the detected locations; summing the applied PDFs to obtain atleast one PDF distribution; and converting the at least one PDFdistribution to image data.